Scrabblette and I played a few games of Hex and Y last night. This was Scrabblette's first time playing and she didn't really get the strategy. (BTW, she subsequently beat me at Bridg-It, but this post is not about that.) After the game (and for a while when I would have preferred to be asleep) I was thinking about strategy for connection games on the hex grid. This post IS about that.
The basic tactic I understand involves the colours on the board above. If I've claimed two "adjacent" red hexes (or yellow, or white) and my opponent has not played on any of the spaces between them, I have an unbreakable connection between them. Hence for several games last night I was playing almost solely on the (let's say) red hexes until Scrabblette realised she'd lost.
Now where we're up to in our understanding of strategy is that the game is won or lost according to who claims the best chain of red hexes. But it occurs to me that the red hexes themselves form a hex grid, and you can make connections on that grid by claiming the blue hexes in this diagram:
And of course the blue hexes form a hex grid... and so on until we can identify exactly the most important hex that the opponent must claim in response to a move - the most important move at the highest level of abstraction. I know, I'm losing people here. Consider this colouring:
Say I'm trying to make a chain from top-left to bottom-right and I make my first move at A. (We're not using a pie rule here, we're not smart enough.) I'd love to make my next move at B, C or D so you should play there instead to prevent me. In fact if you let me play at A, B and D I believe the game is lost for you. So you play at C, I play at D and you play at B. It looks like if I play at B1 you'll have a really hard time getting through. Hmm... what happens next? I haven't figured that out yet.